1123581321 Posted March 27, 2011 Share Posted March 27, 2011 I was wondering if someone could please explain to me what this means: the function tan^-1(x) or arctan(x) is a periodical function with the period of pie = 180(degrees) an analogy etc might be useful to me, thanks. Link to comment Share on other sites More sharing options...
ydoaPs Posted March 27, 2011 Share Posted March 27, 2011 It would be best to look at a graph. If it is periodical over a period, that means it repeats itself. Like a sine wave goes all the way around and back to its starting point in a period of 2π. Link to comment Share on other sites More sharing options...
Bignose Posted March 27, 2011 Share Posted March 27, 2011 Periodic means some function f obeys [math]f(x) = f(x \pm nm)[/math] for any integer n and some value m. The function has the same value when you increase or decrease the input by nm. Arctan isn't periodic, though. Sine and cosine are, though: [math]\sin (x) = \sin (x \pm 2 \pi n )[/math] Link to comment Share on other sites More sharing options...
1123581321 Posted March 27, 2011 Author Share Posted March 27, 2011 im still not sure that i completely understand. but what exactly does the arc (at the start) mean / imply ..? Link to comment Share on other sites More sharing options...
John Cuthber Posted March 27, 2011 Share Posted March 27, 2011 arc tan means the inverse of tangent. So, tan (45 degree) = 1. Arctan (1) =45 degrees. It's a particularly stupid bit of nomenclature Link to comment Share on other sites More sharing options...
DrRocket Posted March 27, 2011 Share Posted March 27, 2011 im still not sure that i completely understand. but what exactly does the arc (at the start) mean / imply ..? In radians the angle is associated with the arc length of an arc at radius 1 subtended by the angle. So arctan is the arc, or angle, that produces some value for the tangent function -- the inverse. Since tan is pi periodic, the inverse is only defined modulo pi. arctan is the inverse of tan restricted to (-pi/2, pi/2). Link to comment Share on other sites More sharing options...
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